\section{Introduction}  
Accordingly to the predictions of the International Technology Roadmap
for Semiconductors, the number of integrated processing elements into
a modern multiprocessors system-on-chip (MPSoC) is increasing
dramatically~\cite{itrs_sysdriver11}. It is foreseen that the
threshold of 1,000 processing cores will be surpassed by the year
2020. A practical demonstration of such a trend can be observed by
considering two prototypes developed by Intel~\cite{vangal_jssc08,
  intel256_ssd14}. The first one, developed in 2008, integrates 80
processing cores in a 65~nm CMOS technology, while the second one,
developed after 5 years, integrates 256 cores in a 22~nm Tri-Gate CMOS
technology. As the number of communicating cores increases, the role
played by the on-chip communication system becomes more and more
important. Both the above prototypes use a Network-on-Chip (NoC) as
interconnection fabric. In fact, the NoC paradigm is considered as the
most viable solution for addressing the communication issues in the
context of manycore architectures~\cite{benini_computer02}.

Unfortunately, due to their multi-hop nature, as the network size
increases, conventional NoCs which use electric point-to-point links,
start to suffer from scalability problems, both in terms of
communication latency and energy.  For facing with such scalability
issues, several emerging interconnect paradigms such as Optical, 3D,
and RF solutions have been proposed~\cite{carloni_nocs09}.  In
particular, a specific class of RF interconnect introduces a wireless
backbone upon traditional wire-based NoC
substrate~\cite{deb_jetcas12}.

The use of the radio medium for on-chip communication is enabled by
means of antennas and transceivers which form the core of a
\emph{radio-hub}. A radio-hub augments the communication capabilities
of a conventional NoC switch/router by allowing it to wireless
communicate with other radio-hubs in a single hop. The reduction of
the average communication hop count, has a positive impact on both
performance and power metrics but, the price to pay, regards the
silicon area due for transceivers and antennas. Another aspect regards
the attenuation introduced by the wireless channel.  Since
electromagnetic waves are propagated in lossy silicon, the power due
to the wireless signaling represent an important contribution of the
entire communication energy budget. In fact, in~\cite{yu_mwscas11} it
has been shown that the transmitter is responsible for about 65\% of
the overall transceiver power consumption, while in~\cite{daly_jssc07}
such contribution is more than 74\%. Thus, wireless communication
results more energy efficient than wired communication when the
communicating nodes are far away each other (in several studies such
a distance has been reported being greater than two hops).

With regards to the amount of transmitting power needed to guarantee a
certain reliability level (usually measured in terms of bit error
rate), a common practice is computing the worst case attenuation and
transmitting using such maximum power level irrespective of the
location of the destination. Furthermore, in the current WiNoC
literature, the radiation pattern of the antenna is considered
isotropic, that is, it is assumed that the antenna exhibits the same
behaviour irrespective of the transmitting/receiving
directions. However, it is well known from antennas theory that the
behaviour of the antenna strongly depends on the direction from/to
which the signal is received/transmitted. Such behaviour is described
by a fundamental antenna parameter, namely, \emph{antenna directivity},
which describes the variation of the transmitting/receiving signal
intensity for different observation angles. The directivity effects,
widely studied in the context of free space communications, have been
recently investigated in the context of intra-chip
communications~\cite{tap_07}. In the context of WiNoCs, however, there
are no works in literature that take into account the directivity
effects, and the antenna orientation is left out from the set of
design parameters to be explored.

In this paper, we analyse the impact of antennas orientation on energy
metrics in WiNoC architectures. Based on such analysis, we formulate
the problem of finding the antennas orientation in such a way to
minimize the total communication energy in the following two
cases. The case in which the information about the applications that
will be mapped on the WiNoC and their communication characteristics
are not known, and the case in which they are known at design time. We
refer to the first case as \emph{general purpose} and the second one
as \emph{application specific}. Further, we also formulate the problem
of finding the antennas orientation in such a way to minimize the
transmitting power for the worst case. This latter problem is
important in the case in which the WiNoC does not implement any
technique for dynamic transmitting power
calibration~\cite{mineo_date14, mineo_date15} and when the same
transmitting power is used for any communicating pairs irrespective of
their position into the WiNoC. Experiments, carried out on
state-of-the-art WiNoC architecture, namely, HmWNoC~\cite{deb_tc13} 
show that important energy saving, up to 80\% can be obtained by 
properly set the orientation of the antennas.

%% Overall, the main contributions of this paper can be summarized
%% as follows:
%% \begin{itemize}
%%   \item 
%% \item This is the first technique which exploit the antenna directivity
%% 	  in the context of WiNoC architecture giving some design guidelines
%% 	  to do this.

%% \item An open source tool, WADET (Wireless Antenna Design Exploration Tool), 
%% 	  has been also developed for applying the optimization methods incorporated
%% 	  in such guidelines.

%% \item It opens the prospective to consider different kind of antennas 
%% 	  with specified occupied area and radiation pattern.
%% \end{itemize}

%% Experimental results conducted with a field solver simulator and with a
%% specific tool for computing energy consumption in a state-of-art WiNoC architecture
%% named msWiNoC, demonstrate an energy reduction up to x\% without, in one of the two
%% guidelines the introduction of additional hardware.

%% The rest of the paper is organized as follow: section II  shows
%% related works in the field of WiNoCs architecture. Section III give
%% the theoretical basis to understand the proposed technique. Section IV
%% shows results from experimental results. Finally Section V concludes
%% the paper.
